Termination w.r.t. Q proof of /home/nowonder/forschung/aprove/satrung/aprove/lpar3/SK90SLASH4.36.trs

Termination w.r.t. Q of the following Term Rewriting System could be proven:

Q restricted rewrite system:
The TRS R consists of the following rules:

a₁(a₁(x)) -> a₁(b₁(a₁(x)))

Q is empty.

↳ QTRS

  ↳ DependencyPairsProof

Q restricted rewrite system:
The TRS R consists of the following rules:

a₁(a₁(x)) -> a₁(b₁(a₁(x)))

Q is empty.

Q DP problem:
The TRS P consists of the following rules:

A₁(a₁(x)) -> A₁(b₁(a₁(x)))

The TRS R consists of the following rules:

a₁(a₁(x)) -> a₁(b₁(a₁(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.

↳ QTRS

  ↳ DependencyPairsProof

    ↳ QDP

      ↳ DependencyGraphProof

Q DP problem:
The TRS P consists of the following rules:

A₁(a₁(x)) -> A₁(b₁(a₁(x)))

The TRS R consists of the following rules:

a₁(a₁(x)) -> a₁(b₁(a₁(x)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph contains 0 SCCs with 1 less node.